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2Who am I Assistant prof. at INSEAD since 2008.Teaching Prices and Markets in the MBA program, Econometrics A, B, Microeconometrics, in the PhD program.Research:Applied empirical work on Urban Economics.Economics of Discrimination.Banking/Competition.Econometric Forecasts.I tend to cold call.

3Goals of my Micro C classesEconomics and psychology have a large number of common interests, but use different toolboxes.Subjective perceptions, gender, culture.Economics and individual rationality.Formation of perceptions using Bayes’ framework.Economics and strategy use very similar tools and have a large number of common interests:Strategic interactions.Strategic interactions with imperfect information.

72. Guess a number Each person gives me a number between 0 and 100.The person who is closest to 2/3 of the average gets a bottle of champagne.Number?What’s the reasoning?Typical outcomes?

82. Guess a number The Bayesian ApproachAssumption of perfect rationality is not consistent with the empirical observations…Assume that players are of one of two types: either rational or random.The random players choose a number between 0 and 100 randomly.What should be the choice of the rational players?Note first that all rational players will choose the same number.Call this number x.Then we use Bayes’ formula.E(numbers) = E(numbers|rational players). P(rational players) + E(numbers|random players).P(random player).Solution?

92. Guess a number Another approach to the problem.“Iterated Elimination of Dominated Strategies”Anyone playing a number between 67 and 100?Anyone playing a number between 44 and 100?Etc…What is the number left?But is everybody thinking so deeply? (Nagel, 2002)Can we explain our empirical results in the MBA classroom? What is students’ depth of thinking?

112. Prisoners’ Dilemma Example #1: Prisoners. RoadmapPlayers, Strategies, and Payoffs.Write the payoff matrix.Are there dominant strategies?What is the Nash equilibrium?Where is the uncertainty?Write the payoff matrix(ces) with uncertainty.What is one Bayesian Nash equilibrium?

13Prisoners The psychology of the game is essential.How does that affect the game? Players’ types? Players’ beliefs?Jim/JohnNot ConfessConfess-2,-2-8,00,-8-5,-5The psychological cost of confessing. If both players have a cost of confessing:Jim/JohnNot ConfessConfess-2,-2-8,0-c0-c,-8-5-c,-5-c

15Bayesian game: Types, Beliefs, Strategies, Payoffs.Type is either {high cost c,low cost c}.Beliefs about the other player’s type are represented by the subjective probability of being of a high cost c of deviation/low cost.Simultaneous move game.Strategy: one action for each type.Payoffs: the payoff matrix for each pair of types of players.

16Bayesian Nash equilibriumis a strategy for each player, for each type, such that: each player’s strategy is a best response to the other player’s strategy given (a) his beliefs about the other player’s type and (b) given the other player’s strategy for each type.

17Bayesian Nash equilibriumWe check that the following is a Bayesian Nash equilibrium:The high cost of deviation player does not confess.The low cost of deviation player confesses.Checking this is an equilibrium:What is Jim’s best response?when he is of a high cost of confessing?when he is of a low cost of confessing?… and when he believes that John is of a high cost with probability p.… and when he assumes the above strategy (blue box) for John.Same question for John.What fraction of games see both players cooperating?

20Price competition: Tiger vs. Singapore AirlinesFlight at 10am on January 23rdAt 4pm the previous day… what should the Tiger and Singapore Airlines pricing people displayon the website? Two pricing points: $200 or $150.Demand for seats: 40.Marginal cost: $20 per seat.Airline with the lowest price sells 40 seats.If equal prices: customers indifferent between the two airlines.Tiger/Singapore AirlinesHigh priceLow price$3600,$36000,$5200$5200,0$2600,$2600

22Singapore Airlines does not know for sure Tiger’s remaining capacityTiger can be of one of two types. Either Unconstrained, or ConstrainedPrior p=P(Constrained).Singapore’s capacity is common knowledge.Check whether the following is a Bayesian Nash equilibrium:The unconstrained Tiger Airways deviates, the constrained Tiger Airways does not deviate; Singapore Airlines does not deviate.“deviate”=“sets a low price.”Under what constraint on p is this a Bayesian Nash equilibrium?

234. Entry Game Example #1: The flatmate. Example #2: Apple vs Samsung.Roadmap for this sectionWrite the sequential game.What is the subgame perfect Nash equilibrium?Where is the uncertainty?Consider the game with no uncertainty, repeated multiple times. What is the subgame perfect Nash equilibrium?What about uncertainty with multiple periods?Takeaways?

24Apple vs SamsungRivals: Handsets are (imperfect) substitutes in the eyes of consumers.Entrant and incumbent?Fighting against the entrant?Cost of fighting?Benefit of fighting?

27Entry Game, “Soft” IncumbentEntrantStay outEnterIncumbent(0,10)FightAccommodate(-5,4)(5,5)Discuss the payoffs. Give at least 2 examples of market competition to which this sequential game may apply.Notice the order of the payoffs. The first mover comes first.What is the subgame perfect Nash equilibrium?

28Entry Game, “Tough” IncumbentEntrantStay outEnterIncumbent(0,10)FightAccommodate(-5,6)(5,5)What is the subgame perfect Nash equilibrium? Such an equilibrium justifies talking about a “tough” incumbent.

29What if we don’t know the incumbent’s type?Prior about the incumbent.We represent this prior with a probability p: The entrant believes that the incumbent is tough with probability p.\Fill in the payoffs below.When does the entrant choose to enter? When does he choose to stay out?EntrantStay outEnterIncumbent( , )FightAccommodate( , )( , )

30Playing the entry game twice… knowing that the incumbent is soft.EntrantEntrantStay outEnterStay outEnterIncumbentIncumbent(0,10)(0,10)FightAccommodateFightAccommodate(-5,4)(5,5)(-5,4)(5,5)Round 1Round 2Would the incumbent fight?

31Playing the entry game twice… knowing that the incumbent is tough.EntrantEntrantStay outEnterStay outEnterIncumbentIncumbent(0,10)(0,10)FightAccommodateFightAccommodate(-5,6)(5,5)(-5,6)(5,5)Round 1Round 2Would the incumbent fight?

33Reputation managementFighting tells potential entrants that you are either tough or a soft guy trying to build his reputation.Accommodating tells potential entrants that you are soft with certainty.➭One discordant piece of information is enough to destroy one’s reputation.“it takes a lifetime to build a reputation and one second to destroy it.” Warren Buffett and many other “wise” guys.

34Playing the entry game twice… not knowing the incumbent’s type.The tough incumbent fights in every period.The soft incumbent fights if…The cost of fighting is smaller than the benefits of building a reputation.What is this cost of fighting?What is the benefit of having a reputation?With a discount factor?What is the meaning of the discount factor?

35Perfect Bayesian Nash EquilibriumAll types play the same strategy.Observing the actions does not bring information on the types.Pooling equilibrium:Tough and soft incumbents fight in the first period.Soft incumbents find it rational to fight in the first period.Separating equilibrium:Tough incumbents fight.Soft incumbents accommodate.Soft incumbents do not find it rational to fight in the first period.Different types play different strategies.Observing the actions gives information about types.

36Playing the Entry game n times… not knowing the incumbent’s type.When there are k periods (think years, quarters), the reputational benefits are multiplied by k (if discount factor is 1), so the earlier the entry, the larger the reputational benefits of fighting.Confident of being present in the market for a large number of years/quarters? The longer the time horizon, the more important reputation is.Solve this with 3 periods.

39Key concepts for this session (1/2)Simultaneous move games with imperfect information.Players, Strategies, Payoffs.Beliefs, Types.Bayesian Nash Equilibrium.Make sure you know the meaning of these concepts.

40Key concepts for this session (2/2)Sequential games with imperfect information.Players, Strategies, Payoffs.Beliefs, Types.Perfect Bayesian equilibrium.Make sure you know the meaning of these concepts.